Rotational diffusion of particles in turbulence

Abstract

In aquatic environments, particles (e.g., sediment or microorganisms) tend to rotate as they move. For example, rotation is an important component of a microorganism's motion and search for food. Using two simple shapes, a sphere and a prolate ellipsoid (i.e., a football), we examined how shape affects rotation. To isolate the effects of rotation from the effects of settling, we made near neutrally buoyant particles (same density as water). We generated turbulence in a laboratory water tank and introduced hundreds of particles, one shape at a time. While the particles were tumbling in the flow, we measured their rotation by using stereoscopic particle image velocimetry (SPIV), a technique that uses a laser to light up tracers embedded in the particles and then takes photos in rapid succession to compute the point velocities inside the particle. Since every part of the body rotates at the same angular speed, we determined all components of the angular velocity from the velocities inside the particles. A series of SPIV images showed how rotation of the particle changes over time in the turbulence. Using the average of many different sets of images, we modeled the change in particle rotation over time as a random walk through the range of possible rotations. We found that ellipsoidal and spherical particles rotated with the same characteristic time, unaffected by shape difference. From this we concluded that the large scales of turbulence govern rotation, rather than the small scales; large eddies, which are unable to differentiate between spheres and ellipsoids, determine rotation.Through laboratory measurements, we compared the rotation of spherical and ellipsoidal particles in homogeneous, isotropic turbulence. We found that the particles' angular velocity statistics are well described by an Ornstein–Uhlenbeck (OU) process. This theoretical model predicts that the Lagrangian autocovariance of particles' angular velocity will decay exponentially. We measured the autocovariance by using stereoscopic particle image velocimetry (SPIV) applied to spherical and ellipsoidal particles whose size was within the inertial subrange of the ambient turbulence. SPIV resolves the motion of points interior to the particles, from which we calculated the solid body rotation of the particles. This provided us with the angular velocity time series for individual particles. Through ensemble statistics, we determined the autocovariance of angular velocity and confirmed that it matches the form predicted by an OU process. We found that in this stochastic framework the autocovariances of both the ellipsoids and spheres are statistically identical, suggesting that rotation is controlled by the large scales of turbulence. We can further use the autocovariance curve to quantify the turbulent rotational diffusivity and discuss its implications for the transport of aquatic organisms in natural turbulence.